Regular Expressions Homework Help

1.We can generalize our construction from a regular expression to an automaton with o-transitions to include expressions that use the extended operators of Section 10.7. That statement is true in principle, since each of those extensions is a shorthand for an “ordinary” regular expression, by which we could replace the extended operator. However, we can also incorporate the extended operators directly into our construction. Show how to modify the construction to cover
a) the ? operator (zero or one occurrences)
b) the + operator (one or more occurrences)
c) character classes.

2.Construct automata with o-transitions for the following regular expressions
a) aaa Hint: Remember to create a new automaton for each occurrence of operand

3.The operand ∅ is not needed in regular expressions, except that without it, we could not find a regular expression whose language is the empty set. Call a regular expression ∅-free if it has no occurrences of ∅. Prove by induction on the number of operator occurrences in a ∅-free regular expression R, that L(R) is not the empty set. Hint: The next section gives an example of an induction on the number of operator occurrences of a regular expression.

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4.If you have UNIX available, write egrep programs to examine the file and find

a) All words that end in dous.
b) All words that have only one vowel.
c) All words that have alternating consonants and vowels.
d) All words that have four or more consecutive consonants.

5.Write expressions for the following character classes.
a) All characters that are operators or punctuation symbols in C. Examples are + and parentheses.
b) All the lower-case vowels.
c) All the lower-case consonants.